Tsunamis have gained worldwide attention over the past decade, primarily because of the destruction caused by two tsunamis: one that killed more than 200,000 people in coastal regions surrounding the Indian Ocean in December 2004; and another that killed 15,000 more and triggered a severe nuclear accident in Japan in March 2011. This talk has three parts. It begins with a description of how tsunamis work: how they are created, how they propagate and why they are dangerous. This part involves almost no mathematics, and should be understandable to everyone. The second part of the talk is about the operational models now being used to provide tsunami warnings and forecasts. These models predict some features of tsunamis accurately, and other features less accurately, as will be discussed. The last part of the talk is more subjective: what public policies could be enacted to mitigate some of the dangers of tsunamis? Much of the material in this talk appeared in a paper by Arcas & Segur, Phil. Trans. Royal Soc. London, 370, 2012.